I'm trying to find an old sci-fi story I remember reading, but cannot recall the name or the author. I thought it was Soviet sci-fi but now I'm not sure, as one of my friends vaguely recalls this from an American author.
The premise: in future, time travel into past is developed and is used to "yank" talented people from the past just before their deaths, to let them finish what they had the potential for, but never got chance to create.
However, to preserve the timeline, after they finish their work they are re-inserted into their original timeline to die.
The protagonist is a writer that had an incurable disease, got taken into the future, cured of the disease, wrote his magnum opus, got to terms with the necessity of his return, and then was re-infected with the disease and re-inserted into past.
Edit: seems like I was misremembering, and the writer above was the only person so transported, it was not a mass program.